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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Differentiable group actions on homotopy spheres. II. Ultrasemifree actions


Author: Reinhard Schultz
Journal: Trans. Amer. Math. Soc. 268 (1981), 255-297
MSC: Primary 57S15; Secondary 57R60, 57S25
MathSciNet review: 632531
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Abstract: A conceptually simple but very useful class of topological or differentiable transformation groups is given by semifree actions, for which the group acts freely off the fixed point set. In this paper, the slightly more general notion of an ultrasemifree action is introduced, and it is shown that the existing machinery for studying semifree actions on spheres may be adapted to study ultrasemifree actions equally well. Some examples and applications are given to illustrate how ultrasemifree actions (i) may be used to study questions not answerable using semifree actions alone, and (ii) provide examples of unusual smooth group actions on spheres with no semifree counterparts.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0632531-6
PII: S 0002-9947(1981)0632531-6
Article copyright: © Copyright 1981 American Mathematical Society